Device manufacturing method, lithographic apparatus, and a computer program

ABSTRACT

A device manufacturing method includes exposing a substrate with a patterned beam of radiation formed by a reticle mounted on a displaceable reticle stage, determining a non-linear function for approximating a height and a tilt profile of a surface of the reticle with respect to the reticle stage, and controlling a displacement of the reticle stage during exposure of the substrate in accordance with the non-linear function.

FIELD

The present invention relates to a method for manufacturing a device, a lithographic apparatus and a computer program.

BACKGROUND

A lithographic apparatus is a machine that applies a desired pattern onto a substrate, usually onto a target portion of the substrate. A lithographic apparatus can be used, for example, in the manufacture of integrated circuits (ICs). In that instance, a patterning device, which is alternatively referred to as a mask or a reticle, may be used to generate a circuit pattern to be formed on an individual layer of the IC. This pattern can be transferred onto a target portion (e.g. comprising part of, one, or several dies) on a substrate (e.g. a silicon wafer). Transfer of the pattern is typically via imaging onto a layer of radiation-sensitive material (resist) provided on the substrate. In general, a single substrate will contain a network of adjacent target portions that are successively patterned. Known lithographic apparatus include so-called steppers, in which each target portion is irradiated by exposing an entire pattern onto the target portion at one time, and so-called scanners, in which each target portion is irradiated by scanning the pattern through a radiation beam in a given direction (the “scanning”-direction) while synchronously scanning the substrate parallel or anti-parallel to this direction. It is also possible to transfer the pattern from the patterning device to the substrate by imprinting the pattern onto the substrate.

Historically, in lithographic tools, a mounting side and a patterned side of a reticle are one and the same, thereby establishing a reticle focal plane at a plane of a reticle stage plate. Thus, knowledge of stage position in six degrees of freedom (DOF) results in knowledge of the reticle patterned surface position in six DOF. The six DOF are X, Y, Z, Rx, Ry, and Rz, as shown in FIG. 2. However, mounting (or clamping) of an extreme ultra violet (EUV) reticle will likely be to a back surface of the reticle (e.g., opposite from the patterned surface). Backside clamping results in a reticle focal plane position relative to the reticle stage that is a function of reticle height and tilt profile. Thus, in contrast to deep ultra violet (DUV) systems, knowledge of the reticle stage position does not resolve where the pattern of the reticle is located in all six DOF. The out-of-plane DOF (Z, Rx, and Ry) cannot be easily determined due to the thickness variation of the reticle. It is desirable to accurately know the position of the patterned side (opposite to the clamped side) of the reticle in all six DOF.

In almost all steppers and scanners, three in-plane DOF (X, Y, and Rz) are determined from typical stage metrology schemes using interferometers. However, three out-of-plane DOF (Z, Ry, and Rx) are more difficult to measure. As discussed above, in an EUV tool, Z, Rx, and Ry should be known with much higher accuracy than in previous lithography tools. The desire for higher accuracy stems from the need to position the pattern on the reticle at a focal plane related to optics of the lithography tool. Also, in some cases, optics are not telecentric at the reticle focal plane, which increases the need for accurately determining the reticle position on the reticle stage to within six DOF. The focal plane is also referred as the best object plane. At the same time, focus should be accurately maintained on the pattern on the reticle even though the reticle has a certain height and tilt profile with respect to the reticle stage. Therefore, measuring the Z position and the out of plane tilts (Rx and Ry) of the patterned side of the reticle in the EUV tool may require tight accuracy.

An embodiment of a measuring system is published in U.S. Pat. No. 6,934,005. The published system comprises an interferometer arranged to provide input data related to a height and tilt profile of the reticle surface. These data are subsequently processed by a suitable computer program to linearly approximate the height and the tilt profile of the reticle surface. For this purpose, the reticle comprises two reflective paths arranged substantially at opposite sides of the reticle, notably extending along the y-direction of a coordinate system assigned to the reticle and the reticle stage, see FIG. 2. The interferometer data is used to approximate the reticle surface, which is used for controlling a linear displacement of the reticle stage during a suitable exposure of the substrate.

It is a disadvantage of the known method that considerable distortions may occur when the reticle stage moves linearly during the exposure of the substrate.

SUMMARY

It is desirable to provide a device manufacturing method, particularly for Extreme Ultra Violet (EUV) range, wherein distortion maps occurring at the best object plane are substantially reduced.

According to an aspect of the invention, a device manufacturing method includes exposing a substrate with a patterned beam of radiation formed by a reticle mounted on a displaceable reticle stage, determining a non-linear function for approximating a height and a tilt profile of a surface of the reticle with respect to the reticle stage, and controlling a displacement of the reticle stage during exposure of the substrate in accordance with the non-linear function.

According to an aspect of the invention, a lithographic apparatus is arranged to project a pattern from a reticle onto a substrate. The apparatus includes a displaceable reticle stage constructed and arranged to support the reticle. The reticle has a patterned side. The apparatus also includes a detector constructed and arranged to determine data related to a height and a tilt profile of a surface of the reticle with respect to the reticle stage, and a computing device configured to approximate the height and the tilt profile by a non-linear function using the data. The apparatus further includes a controller constructed and arranged to control a displacement of the reticle stage during exposure of the substrate in accordance with the non-linear function.

According to an aspect of the invention, a lithographic apparatus includes an illumination system configured to condition a radiation beam, and a support constructed to support a patterning device. The patterning device is capable of imparting the radiation beam with a pattern in its cross-section to form a patterned radiation beam. The support is displaceably arranged. The apparatus also includes a substrate table constructed to hold a substrate, a projection system configured to project the patterned radiation beam onto a target portion of the substrate, and a detector for determining data related to a height and a tilt profile of a surface of the patterning device with respect to the support. The apparatus further includes a computing device configured to approximate the surface of the patterning device by a non-linear function using the data; and a controller constructed and arranged to control a displacement of the support during exposure of the substrate in accordance with the non-linear function.

According to an aspect of the invention a computer program includes instructions for causing a processor to execute the steps of a device manufacturing method that includes exposing a substrate with a patterned beam of radiation formed by a reticle mounted on a displaceable reticle stage, determining a non-linear function for approximating a height and a tilt profile of a surface of the reticle with respect to the reticle stage, and controlling a displacement of the reticle stage during exposure of the substrate in accordance with the non-linear function.

According to an aspect of the invention, a device manufacturing method includes patterning a beam of radiation with a patterning device that is carried by a support, projecting the patterned beam of radiation onto a target portion of a substrate, determining data related to a height and a tilt profile of a surface of the patterning device with respect to the support, approximating the surface of the patterning device by a non-linear function using the data, and controlling a displacement of the support during exposure of the substrate in accordance with the non-linear function.

BRIEF DESCRIPTION OF THE DRAWINGS

Embodiments of the invention will now be described, by way of example only, with reference to the accompanying schematic drawings in which corresponding reference symbols indicate corresponding parts, and in which:

FIG. 1 depicts a lithographic apparatus according to an embodiment of the invention;

FIG. 2 depicts in a schematic way a coordinate system assigned with a reticle of the apparatus of FIG. 1;

FIG. 3 depicts in a schematic way an exposure slit and an effect of a height offset (z-offset);

FIG. 4 depicts in a schematic way the best object plane aligned to the reticle surface;

FIG. 5 depicts in a schematic way an embodiment of a computational grid defined on the slit; and

FIG. 6 depicts in a schematic way an embodiment of a lithographic apparatus according to the invention.

DETAILED DESCRIPTION

FIG. 1 schematically depicts a lithographic apparatus according to an embodiment of the invention. The apparatus comprises: an illumination system (illuminator) IL configured to condition a radiation beam B, notably an EUV radiation; a support structure (e.g. a mask table) MT constructed to support a patterning device (e.g. a mask) MA and connected to a first positioner PM configured to accurately position the patterning device in accordance with certain parameters; a substrate table (e.g. a wafer table) WT constructed to hold a substrate (e.g. a resist-coated wafer) W and connected to a second positioner PW configured to accurately position the substrate in accordance with certain parameters; and a projection system (e.g. a refractive projection lens system) PS configured to project a pattern imparted to the radiation beam B by patterning device MA onto a target portion C (e.g. comprising one or more dies) of the substrate W.

The illumination system may include various types of optical components, such as refractive, reflective, magnetic, electromagnetic, electrostatic or other types of optical components, or any combination thereof, for directing, shaping, or controlling radiation.

The support structure supports, i.e. bears the weight of, the patterning device. It holds the patterning device in a manner that depends on the orientation of the patterning device, the design of the lithographic apparatus, and other conditions, such as for example whether or not the patterning device is held in a vacuum environment. The support structure can use mechanical, vacuum, electrostatic or other clamping techniques to hold the patterning device. The support structure may be a frame or a table, for example, which may be fixed or movable as required. The support structure may ensure that the patterning device is at a desired position, for example with respect to the projection system. Any use of the terms “reticle” or “mask” herein may be considered synonymous with the more general term “patterning device.”

The term “patterning device” used herein should be broadly interpreted as referring to any device that can be used to impart a radiation beam with a pattern in its cross-section such as to create a pattern in a target portion of the substrate. It should be noted that the pattern imparted to the radiation beam may not exactly correspond to the desired pattern in the target portion of the substrate, for example if the pattern includes phase-shifting features or so called assist features. Generally, the pattern imparted to the radiation beam will correspond to a particular functional layer in a device being created in the target portion, such as an integrated circuit.

The patterning device may be transmissive or reflective. Examples of patterning devices include masks, programmable mirror arrays, and programmable LCD panels. Masks are well known in lithography, and include mask types such as binary, alternating phase-shift, and attenuated phase-shift, as well as various hybrid mask types. An example of a programmable mirror array employs a matrix arrangement of small mirrors, each of which can be individually tilted so as to reflect an incoming radiation beam in different directions. The tilted mirrors impart a pattern in a radiation beam which is reflected by the mirror matrix.

The term “projection system” used herein should be broadly interpreted as encompassing any type of projection system, including refractive, reflective, catadioptric, magnetic, electromagnetic and electrostatic optical systems, or any combination thereof, as appropriate for the exposure radiation being used, or for other factors such as the use of an immersion liquid or the use of a vacuum. Any use of the term “projection lens” herein may be considered as synonymous with the more general term “projection system”.

As here depicted, the apparatus is of a reflective type (e.g. employing a reflective mask). Alternatively, the apparatus may be of a transmissive type (e.g. employing a transmissive mask).

The lithographic apparatus may be of a type having two (dual stage) or more substrate tables (and/or two or more mask tables). In such “multiple stage” machines the additional tables may be used in parallel, or preparatory steps may be carried out on one or more tables while one or more other tables are being used for exposure.

The lithographic apparatus may also be of a type wherein at least a portion of the substrate may be covered by a liquid having a relatively high refractive index, e.g. water, so as to fill a space between the projection system and the substrate. An immersion liquid may also be applied to other spaces in the lithographic apparatus, for example, between the mask and the projection system. Immersion techniques are well known in the art for increasing the numerical aperture of projection systems. The term “immersion” as used herein does not mean that a structure, such as a substrate, must be submerged in liquid, but rather only means that liquid is located between the projection system and the substrate during exposure.

Referring to FIG. 1, the illuminator IL receives a radiation beam from a radiation source SO. The source and the lithographic apparatus may be separate entities, for example when the source is an excimer laser. In such cases, the source is not considered to form part of the lithographic apparatus and the radiation beam is passed from the source SO to the illuminator IL with the aid of a beam delivery system comprising, for example, suitable directing mirrors and/or a beam expander. In other cases the source may be an integral part of the lithographic apparatus, for example when the source is a mercury lamp. The source SO and the illuminator IL, together with the beam delivery system if required, may be referred to as a radiation system.

The illuminator IL may comprise an adjuster for adjusting the angular intensity distribution of the radiation beam. Generally, at least the outer and/or inner radial extent (commonly referred to as σ-outer and σ-inner, respectively) of the intensity distribution in a pupil plane of the illuminator can be adjusted. In addition, the illuminator IL may comprise various other components, such as an integrator and a condenser. The illuminator may be used to condition the radiation beam, to have a desired uniformity and intensity distribution in its cross-section.

The radiation beam B is incident on the patterning device (e.g., mask MA), which is held on the support structure (e.g., mask table MT), and is patterned by the patterning device. Having traversed the mask MA, the radiation beam B passes through the projection system PS, which focuses the beam onto a target portion C of the substrate W. With the aid of the second positioner PW and position sensor IF2 (e.g. an interferometric device, linear encoder or capacitive sensor), the substrate table WT can be moved accurately, e.g. so as to position different target portions C in the path of the radiation beam B. Similarly, the first positioner PM and another position sensor IF1 can be used to accurately position the mask MA with respect to the path of the radiation beam B, e.g. after mechanical retrieval from a mask library, or during a scan. In general, movement of the mask table MT may be realized with the aid of a long-stroke module (coarse positioning) and a short-stroke module (fine positioning), which form part of the first positioner PM. Similarly, movement of the substrate table WT may be realized using a long-stroke module and a short-stroke module, which form part of the second positioner PW. In the case of a stepper (as opposed to a scanner) the mask table MT may be connected to a short-stroke actuator only, or may be fixed. Mask MA and substrate W may be aligned using mask alignment marks M1, M2 and substrate alignment marks P1, P2. Although the substrate alignment marks as illustrated occupy dedicated target portions, they may be located in spaces between target portions (these are known as scribe-lane alignment marks). Similarly, in situations in which more than one die is provided on the mask MA, the mask alignment marks may be located between the dies.

The depicted apparatus could be used in at least one of the following modes:

1. In step mode, the mask table MT and the substrate table WT are kept essentially stationary, while an entire pattern imparted to the radiation beam is projected onto a target portion C at one time (i.e. a single static exposure). The substrate table WT is then shifted in the X and/or Y direction so that a different target portion C can be exposed. In step mode, the maximum size of the exposure field limits the size of the target portion C imaged in a single static exposure.

2. In scan mode, the mask table MT and the substrate table WT are scanned synchronously while a pattern imparted to the radiation beam is projected onto a target portion C (i.e. a single dynamic exposure). The velocity and direction of the substrate table WT relative to the mask table MT may be determined by the (de-)magnification and image reversal characteristics of the projection system PS. In scan mode, the maximum size of the exposure field limits the width (in the non-scanning direction) of the target portion in a single dynamic exposure, whereas the length of the scanning motion determines the height (in the scanning direction) of the target portion.

3. In another mode, the mask table MT is kept essentially stationary holding a programmable patterning device, and the substrate table WT is moved or scanned while a pattern imparted to the radiation beam is projected onto a target portion C. In this mode, generally a pulsed radiation source is employed and the programmable patterning device is updated as required after each movement of the substrate table WT or in between successive radiation pulses during a scan. This mode of operation can be readily applied to maskless lithography that utilizes a programmable patterning device, such as a programmable mirror array of a type as referred to above.

Combinations and/or variations on the above described modes of use or entirely different modes of use may also be employed.

The lithographic apparatus further comprises a detector D for determining measurement data related to a height and a tilt profile of the reticle surface with respect to the reticle stage; a computing device or processor CM for approximating the height and the tilt profile by a non-linear function and a controller CT for controlling a displacement of the reticle stage during exposure of the substrate in accordance with the non-linear function. The controller CT is arranged to displace the reticle stage during the exposure of a wafer in accordance with the non-linear function calculated by the computing device or processor CM for approximating the height and the tilt profile of the reticle surface based in the measured data. The computing device CM employed herein should be broadly construed, and can be, for example, a general purpose computer, hardware, software, a processor, or any combination thereof.

The technical measure of the present disclosure is based on a recognition that a substantial reduction of the distortion field in the best object plane is obtained by taking into account more than two degrees of freedom associated with a set point on the reticle surface and by controlling a displacement of the reticle stage in accordance therewith.

In practice, a reticle has a non-linear height and tilt profile with respect to the reticle stage surface. The reticle surface can be mapped, for example, using a technique in accordance with U.S. Pat. No. 6,934,005, hereby incorporated by reference in its entirety. A suitable interferometer system may be used, which includes, for example, two interferometers. Each interferometer is arranged to project an illuminating light from suitable illumination devices towards the reticle. The illumination device may comprise light sources, lasers, or the like with or without focusing or expanding optical devices. In accordance with the known technique, a first set of interferometric measuring beams from the first interferometer are reflected from reflecting portions of the reticle thereby representing a height and a tilt profile of the reticle surface. The reflected beams are received by suitable detectors of the interferometer. Signals corresponding to the detected beams may be advantageously stored in a storage device either before or after being processed. A second set of interferometric measuring beams from the second interferometer are reflected from suitable positions on the reticle stage and detected by suitable detectors. Signals correlating to the detected beams may then be stored in a storage unit.

The data thus obtained pertain to the reticle height and tilt profiles and are subsequently used in the method according to embodiments of the invention for approximating the reticle surface with a non-linear function. Upon an event, the information on the height and tilt profiles of the reticle is established, for example, by using a suitably arranged computing device, and an EUV reticle leveling functionality, arranged, notably, as a suitable computer program, is advantageously arranged to determine a reticle x-tilt Rx, a reticle z-height map z(y) or YTZ(y), and a reticle y-roll Ryy. The reticle y-roll is defined as a difference of y-tilt between the y-endpoints of the reticle. Further, a reticle y-tilt map Ry(y) is established. It is noted that other degrees of freedom of the reticle like the absolute tilt Ry and the absolute height z are determined by a suitable reticle alignment.

Upon an event the non-linear function approximating the reticle surface is established, the exposure of the substrate may be commenced, during which the reticle stage is displaced in accordance with the non-linear function, thereby compensating for the non-linear height and tilt profile of the reticle surface. It has been found that due to the technical measure of the present disclosure, the distortion map of the image is substantially reduced.

In an embodiment of the invention for determining the non-linear function, the following steps may be undertaken: a first dataset corresponding to a height and a tilt data of the reticle is determined on a first grid; a second dataset corresponding to a number of reticle stage set points is determined on a second grid; and a sequence of the set points is fitted by the non-linear function.

A number of EUV specific design features are responsible for distortion effects due to a certain reticle height and/or a tilt profile, namely the fact that the reticle is reflective, secondly due to non-telecentricity of the optical axis and a diverging shape of the EUV light bundle, and finally, a portion of the light beam to be projected on the reflective reticle is curved. This portion of the light beam is also referred to as an exposure slit. FIG. 3 shows in a schematic way the exposure slit and an effect of a height offset (z-offset) of the object leading to magnification and y-translation.

In order to compensate for the influence of the z-offset on the quality of the image in the best object plane, and for determining the non-linear function, a first dataset corresponding to a height and a tilt data of the reticle is determined on a first grid, a second dataset corresponding to a number of reticle stage set points is determined on a second grid, and a sequence of set points is fitted by the non-linear function. A detailed description of this embodiment is given with respect to FIG. 4 below.

In a further embodiment of the invention, the least squares fit is used for the step of determining the second dataset, thereby fitting the first grid and the second grid.

In order to project the best object plane to the surface of the reticle at the positions of the set points, first, a curved grid over the slit is defined with fixed x-coordinates and y-pitches, see FIG. 5. The grid starts at the bottom and runs upwards until it reaches the top. Preferably, the least squares fit comprises a system of linear equations, whereby the object area on the reticle has substantially the same slit shape and substantially the same slit grid.

Advantages of an application of least squares fit relate first to an automatic filtering of isolated pronounced peaks in the established height profile of the reticle surface and, second, to taking into account curvature of the slit.

Preferably, for the non-linear function, a suitable polynomial profile is selected. The polynomial profile is generated by using the established data for the variables Z_(fit), R_(y,fit) and R_(x,fit). More preferably, the polynomial profile comprises a plurality of 4^(th) order polynomials, smoothly connected to each other. Such a function can be referred to as quartic spline. Mathematic functions, like splines are known per se in the art and their properties will not be explained here in detail. The controlling of the displacement of the reticle stage during exposure of the substrate is preferably carried out in accordance with the quartic (4^(th) order) spline.

Preferably, the lithographic apparatus according to embodiments of the invention comprises an interferometer arranged to determine measurement data for establishing the non-linear function approximating a surface of the reticle.

FIG. 2 presents in a schematic way a coordinate system assigned with the reticle. FIG. 2 shows six degrees of freedom (DOF) for a reticle 100 mounted on a reticle stage 105 and oriented in or parallel to an X-Y plane according to embodiments of the present invention. Again, the six DOF are X (along the X axis), Y (along the Y axis), Z (along the Z axis), Rx (rotation around the X axis), Ry (rotation around the Y axis), and Rz (rotation around the Z axis). The more easily determinable DOF are the X, Y, and Rz based on a reticle stage's movements. In the embodiments discussed below, the DOF that are the focus of the discussion below are Z, Ry and Rx. It is to be appreciated that any DOF can be determined by the apparatus and methods below if the orientation of the reticle 100 is changed. The paths 101 and 102 are arranged as reflective portions of the reticle surface thereby enabling suitable measurements by means of an interferometer.

FIG. 3 depicts in a schematic way the exposure slit and an effect of a height offset (z-offset) of the reticle on the slit shape at the best object plane. FIG. 3 shows schematically a portion of an arc 31 on which the slit shape 33 is defined. A light beam (not shown) is usually arc-shaped having a radius 32 a. The slit 33 is characterized by a half-angle θ and a thickness 35. It is noted that the object side of a projection system is non-telecentric since the illumination field on a reticle (not shown) is shifted off-axis from the projection system (not shown) and the projection beam enters the projection system at an angle with respect to the optical axis of the projection system.

Due to the non-telecentricity of the optical system of the lithographic apparatus, although deviation from telecentricity is preferably arranged to be as small as possible, local vertical z-deformations of the reticle result in horizontal (X or Y) distortions of the image at the best object plane, which is schematically illustrated in the right portion of FIG. 3. The light beam 32 is expected to bounce off at a substantially flat reflective reticle 38 and to propagate in a direction 32′. Due to the height variation Δz of the real reticle 34 with respect to the flat reticle 38, the light beam propagates in a direction 32″ thereby causing a reduction of the slit shape 36 at the best object plane when the reticle has a z-displacement. It is noted that the slit shape is reduced for positive displacements (+z), otherwise the slit shape is enlarged. It is also noted that due to z-offset of the reticle, the slit shape is also displaced by a distance 37 in the y-direction.

FIG. 4 depicts in a schematic way the best object plane 43, 45, 47 aligned to the reticle surface 42. In order to enable the reticle stage to perform corrections for the height and tilt profile of the reticle, a reticle height map and tilt map are determined. This may be done in accordance with a method using interferometers, such as described in U.S. Pat. No. 6,934,005. The established height and tilt profiles of the reticle constitute input data for a reticle leveling unit, which is arranged to compute reticle stage x-tilt values Rx, reticle stage z position and reticle stage y-tilt Ry. It should be understood that reticle stage set points represent a spatial position and tilt of the reticle stage. The reticle stage points are usually defined as a position of an origin of the reticle zero coordinate system (RZCS) in the reticle stage coordinate system (RSCS). In FIG. 4, the reticle stage set points are defined as a position of the origin of the best object plane coordinate system with respect to the origin of the reticle stage coordinate system.

In order to compute a function resolving the alignment between the best object plane and the reticle surface, a number of set points y_(i), y_(i+1), y_(i+2), etc. defined on the reticle stage surface are fitted to the reticle 42. Each set point is characterized by a number of calculated variables, namely height z_(i), a first tilt R_(x,i) and a second tilt R_(y,i). Preferably, these parameters are calculated using a least squares fit of the reticle surface to the best object plane, it being explained in more detail with reference to FIG. 5.

FIG. 5 depicts in a schematic way an embodiment of a computational grid defined on the slit. The slit 51 is approximated by a curved grid constituting points 51 a . . . 51 n, which may be chosen with a constant x and y pitches. It is noted that the top surface 52 and bottom surface 54 of the grid constitute respective sections of a circle and therefore don't run parallel with constant offset in the y-direction. The grid is conveniently formed by seeding the grid points at one surface, for example, the surface 52, and by expanding it until the second surface 54 is reached. The origin of the slit grid is schematically denoted by 53. In accordance with the technical measure of the present disclosure, the first dataset corresponding to a height and a tilt data of the reticle is defined on the first grid 57. The second dataset, corresponding to a number of reticle stage set points 56 is determined on a second grid 56. The first grid 57 and the second grid 56 have a mutual origin 55. Both grids 56 and 57 are defined on the y-axis of the reticle coordinate system RCS.

Alignment of the slit shaped area in the best object plane (BOP) to the slit shaped area on the reticle, is performed as follows. Let RZCS be “framework” coordinates with respect to which the reticle stage moves and is positioned. Let x _(rzcs) be coordinates in the RZCS and let x _(rscs) be coordinates in the reticle stage coordinate system (RSCS). The 3D transformation equation of the reticle stage coordinate system (RSCS) to the reticle zero coordinate system (RZCS) is written as x _(rzcs) =T _(e) ·T·( x _(rscs) −M _(t) ·t+e _(rs)). Here, the diagonal matrix M _(t) is the reticle stage interferometer scaling. Here, e _(rs) is the reticle stage zeroing offset and T _(e) is the reticle stage zeroing rotation offset matrix. Here the infinitesimal rotation matrix

$\underset{\_}{\underset{\_}{T}} = \begin{bmatrix} 1 & {- T_{z}} & T_{y} \\ T_{z} & 1 & {- T_{x}} \\ {- T_{y}} & T_{x} & 1 \end{bmatrix}$ and vector t=(t_(x), t_(y), t_(z)) are transformation parameters. The (vertical) out-of-plane components T_(y), T_(x) and t_(z) of respectively T and t are the out-of-plane reticle stage set points.

Let x _(o) be a coordinate in the best object plane coordinate system (OPCS). The 3D transformation equation of OPCS to the RZCS is x _(rzcs) =R _(o) ·x _(o) +C _(o), where the matrix R _(o) and the vector C _(o) are the transformation parameters. In the following, square brackets behind a symbol, indicate that it is a function of the value between the brackets.

Let x _(rcs) be coordinates in the reticle coordinate system (RCS) and y_(rcs) the corresponding y-coordinate. The 3D transformation equation of the RCS the RSCS is x _(rscs) =M·R[y _(rcs) ]·x _(rcs) +C _(r) +YTZ[y _(rcs) ]·e _(z). Here M is a diagonal magnification matrix. Here C _(r) is a translation parameter, e _(z) is the unit vector in the z-direction and YTZ[y_(rcs)] is the reticle height map function. Here

${{\underset{\_}{\underset{\_}{R}}\left\lbrack y_{rcs} \right\rbrack} = \begin{bmatrix} 1 & {- R_{z}} & {R_{y} + {y_{r} \cdot R_{yy}} + {{YRY}\left\lbrack y_{rcs} \right\rbrack}} \\ R_{z} & 1 & {- R_{x}} \\ {{- R_{y}} - {y_{r} \cdot R_{yy}} - {{YRY}\left\lbrack y_{rcs} \right\rbrack}} & R_{x} & 1 \end{bmatrix}},$ is a matrix valued function specifying an infinitesimal rotation depending on parameters: R_(x), R_(y), R_(z), roll R_(yy) and reticle y-tilt map function YRY[y_(rcs)].

Let x _(r)=(0, y_(r), 0) be the position of the slit shaped object area on the reticle in RCS, it lying along the y-axis. The following formulation of the alignment problem at x _(r) is obtained by writing down the 3D transformation equation between the OPCS and the RCS, as an alignment problem in the RSCS: M _(t) ·t+e _(rs) +T ⁻¹ ·T _(e) ⁻¹·( R _(o) ·x _(o) +C _(o))= M·R[x _(r) +x ]·( x _(r) +x )+ C _(r) +YTZ[x _(r) +x]·e _(z)  (1) and setting x=x _(o). Restrict x to the xy-plane. The right hand side of the equation is the reticle surface in the RSCS. The left hand side defines the best object plane in the RSCS as a first order polynomial in x_(o). The problem is to find the out-of-plane tilts T_(y), T_(x) and the out-of-plane position t_(z), by fitting the slit shaped area in the BOP to the slit shaped area on reticle surface located at x _(r) in the RCS.

In the following this fit will be performed by the method of LSQ: Set x=x _(o) in Equation (1). Let (x_(i), y_(i)) be the grid for the coordinates x covering the slit shaped object area in the BOP, see item 51 in FIG. 5. For a suitable grid, define a grid, consisting of equidistant gridlines of fixed x-value, where every grid line starts at the bottom of the slit shaped area and runs upward with fixed y-pitch until it reaches the top of the area. The fitting problem can be formulated on this grid by the following set of linear equations for the vertical (out of plane) position z_(fit) and tilts R_(y,fit) and R_(x,fit) of the BOP in the local RSCS: z _(fit) −R _(y,fit) ·x _(i) +R _(x,fit) ·y _(i) =z _(i), where i indexes all grid points  (2) This linear set of equations can be solved as an LSQ fitting problem. Solving the equations by using a singular value decomposition would be a suitable method. The right hand side of Equation (2) is obtained by evaluating the z-component of the right hand side of Equation (1) at the grid points (x_(i), y_(i)):

z_(i) = C_(r)^(z) − R_(y) ⋅ x_(i) + R_(x) ⋅ (y_(i) + y_(r)) − R_(yy) ⋅ x_(i) ⋅ (y_(i) + y_(r)) + YTZ[y_(i) + y_(r)] − YRY[y_(i) + y_(r)] ⋅ x_(i). Here the z-component on the diagonal of M has been set to one. Comparing the out-of-plane position z_(fit) and tilts R_(y,fit) and R_(x,fit) with those in the z-component of the left hand side of Eq. (1) leads to z _(fit) =t _(z) +e _(rs) ^(z)+(T _(y) +T _(e) ^(y))·C _(O) ^(x)−(T _(x) +T _(e) ^(x))·C _(o) ^(y) +C _(o) ^(z) R _(y,fit) =−T _(y) −T _(e) ^(y) +R _(o) ^(y) R _(x,fit) =−T _(x) −T _(e) ^(x) +R _(o) ^(x)  (3) Here the z-component on the diagonal of M _(t) has been set to one. The vertical set point values t_(z), T_(y) and T_(x) can be determined from Equation (3).

Preferably, a polynomial profile is generated by using the established data for the variables z_(fit), R_(y,fit) and R_(x,fit). More preferably, the polynomial profile comprises a sequence of concatenated 4^(th) order polynomials, smoothly connected to each other. Such a function can be referred to as quartic (4^(th) order) spline. Mathematic functions, like splines are known per se in the art and their properties will not be explained here in detail. The controlling of the displacement of the reticle stage during exposure of the substrate is preferably carried out in accordance with the thus obtained quartic spline.

FIG. 6 depicts in a schematic way an embodiment of a lithographic apparatus according to the invention. FIG. 6 shows a portion 600 of a lithography tool according to embodiments of the present invention. Portion 600 includes a reticle stage 602 with a backside clamped reticle 604 that has a pattern 606. Although not drawn to scale, an interferometer system 608 includes two interferometers 608A and 608B. It is noted that it is also possible to use a single interferometer arranged to be used in a dual mode. Each interferometer 608A and 608B projects illuminating (I) light from illumination devices 610 towards portion 600. In various embodiments, illumination devices 610 can be light sources, lasers, or the like with or without focusing or expanding optical devices. A first set of interferometric measuring beams RSZ1 and RSZ2 from first interferometer 608A are reflected from first 612 and second 614 positions, respectively, on reticle 604. First position 612 is adjacent a first side of pattern 606 and second position 614 is adjacent a second side of pattern 606. The reflected beams are received by detectors (D) 616. Signals corresponding to the detected beams are stored in a storage device 618 either before or after being processed by controller 620.

A second set of interferometric measuring beams RSZ3 and RSZ4 from second interferometer 608B are reflected from first 622 and second 624 points, respectively, on reticle stage 602 and detected by detectors 616. Signals correlating to the detected beams are then stored in storage 618. In the embodiments shown and described above, all four measuring points, 612, 614, 622, and 624 substantially lie along a line having a same Y value. In other embodiments, this may be required.

In other embodiments, signals represent an interferometric measurement based on either intensity, phase, distance, or the like of two related beams (i.e., RSZ1 and RSZ2 or RSZ3 and RSZ4) being compared. A resulting signal from the comparison corresponds to parameters (e.g., position, orientation, tilt, etc.) of either reticle stage 602 or reticle 604. In various embodiments, the four interferometer beams RSZ1-RSZ4 are used to determine two DOF (Z and Ry) of the patterned surface 606 of reticle 604. In these embodiments, Z is a direction about normal to the patterned surface 606 and parallel to the lithographic tool's optical axis. Also, in these embodiments, Ry is a rotation about a scan axis of the reticle stage 602. As described above, two interferometer beams (RSZ1 and RSZ2) reflect off of pattern surface 606 of reticle 604 on either side of the pattern 606.

Also, in various embodiments, the other two interferometer beams (RSZ3 and RSZ4) are positioned to reflect off of surfaces on the reticle stage 602. There are numerous options for the configuration of these reflective surfaces. In some embodiments, a first reflective surface (e.g., with point 622) of reticle stage 602 can be oriented in or parallel to the X-Y plane to give Z position feedback. Then, a second reflective surface (e.g., with point 624) of the reticle stage 602 can be oriented in or parallel to the X-Y plane. Alternate configurations are possible where the second reflective surface of reticle stage 602 can be oriented in or parallel to a Y-Z plane. Then, the second surface yields Ry stage position information. In further alternative embodiments, various other orientations exist where calculations would yield Z and Ry values. The lithographic tool would typically look at the difference between two interferometers (e.g., dual interferometer 608 or interferometers 608A and 608B) with separation in either the X or Z directions, thus giving Ry information.

Although specific reference may be made in this text to the use of lithographic apparatus in the manufacture of ICs, it should be understood that the lithographic apparatus described herein may have other applications, such as the manufacture of integrated optical systems, guidance and detection patterns for magnetic domain memories, flat-panel displays, liquid-crystal displays (LCDs), thin-film magnetic heads, etc. The skilled artisan will appreciate that, in the context of such alternative applications, any use of the terms “wafer” or “die” herein may be considered as synonymous with the more general terms “substrate” or “target portion”, respectively. The substrate referred to herein may be processed, before or after exposure, in for example a track (a tool that typically applies a layer of resist to a substrate and develops the exposed resist), a metrology tool and/or an inspection tool. Where applicable, the disclosure herein may be applied to such and other substrate processing tools. Further, the substrate may be processed more than once, for example in order to create a multi-layer IC, so that the term substrate used herein may also refer to a substrate that already contains multiple processed layers.

Although specific reference may have been made above to the use of embodiments of the invention in the context of optical lithography, it will be appreciated that the invention may be used in other applications, for example imprint lithography, and where the context allows, is not limited to optical lithography. In imprint lithography a topography in a patterning device defines the pattern created on a substrate. The topography of the patterning device may be pressed into a layer of resist supplied to the substrate whereupon the resist is cured by applying electromagnetic radiation, heat, pressure or a combination thereof. The patterning device is moved out of the resist leaving a pattern in it after the resist is cured.

The terms “radiation” and “beam” used herein encompass all types of electromagnetic radiation, including ultraviolet (UV) radiation (e.g. having a wavelength of or about 365, 355, 248, 193, 157 or 126 nm) and extreme ultra-violet (EUV) radiation (e.g. having a wavelength in the range of 5-20 nm), as well as particle beams, such as ion beams or electron beams.

The term “lens”, where the context allows, may refer to any one or combination of various types of optical components, including refractive, reflective, magnetic, electromagnetic and electrostatic optical components.

While specific embodiments of the invention have been described above, it will be appreciated that the invention may be practiced otherwise than as described. For example, the invention may take the form of a computer program containing one or more sequences of machine-readable instructions describing a method as disclosed above, or a data storage medium (e.g. semiconductor memory, magnetic or optical disk) having such a computer program stored therein.

The descriptions above are intended to be illustrative, not limiting. Thus, it will be apparent to one skilled in the art that modifications may be made to the invention as described without departing from the scope of the claims set out below. 

1. A device manufacturing method comprising: exposing a substrate with a patterned beam of radiation formed by a reticle mounted on a displaceable reticle stage; determining a non-linear function that defines an approximation of a surface of the reticle with respect to the reticle stage based on a height and a tilt profile of the surface of the reticle by: determining a first dataset corresponding to height and tilt data of the reticle on a first grid; determining a second dataset corresponding to a number of reticle stage set points on a second grid; and fitting a sequence of the reticle stage set points by the non-linear function; and controlling a displacement of the reticle stage during exposure of the substrate in accordance with the non-linear function.
 2. The method of claim 1, wherein a least squares fit is used for the determining the second dataset.
 3. The method of claim 2, wherein the least squares fit fits the first grid and the second grid.
 4. The method of claim 1, wherein the first dataset is determined based on interferometer measurements.
 5. A lithographic apparatus arranged to project a pattern from a reticle onto a substrate, the apparatus comprising: a displaceable reticle stage configured to support the reticle, the reticle having a patterned side; a detector configured to determine data related to a height and a tilt profile of a surface of the reticle with respect to the reticle stage; a computing device configured to approximate the surface of the reticle based on the height and the tilt profile and illumination effects due to curvature of an illumination slit, the surface approximation defined by a non-linear function using the data, the non-linear function determined by: a first dataset corresponding to height and tilt data of the reticle on a first grid; a second dataset corresponding to a number of reticle stage set points on a second grid; and a fit between the first dataset and the second dataset; and a controller configured to control a displacement of the reticle stage during exposure of the substrate in accordance with the non-linear function.
 6. The apparatus of claim 5, wherein the detector comprises an interferometer.
 7. A lithographic apparatus comprising: an illumination system configured to condition a radiation beam; a support configured to support a patterning device, the patterning device being capable of imparting the radiation beam with a pattern in its cross-section to form a patterned radiation beam, and the support being displaceably arranged; a substrate table configured to hold a substrate; a projection system configured to project the patterned radiation beam onto a target portion of the substrate; a detector configured to determine data related to a height and a tilt profile of a surface of the patterning device with respect to the support; a computing device configured to approximate the surface of the patterning device, the surface approximation defined by a non-linear function using the data and accounting for illumination effects due to curvature of an illumination slit, the non-linear function determined by: a first dataset corresponding to height and tilt data of the reticle on a first grid; a second dataset corresponding to a number of reticle stage set points on a second grid; and a fit between the first dataset and the second dataset; and a controller constructed and arranged to control a displacement of the support during exposure of the substrate in accordance with the non-linear function.
 8. The lithographic apparatus of claim 7, wherein the detector comprises an interferometer.
 9. The lithographic apparatus of claim 7, wherein the computing device comprises hardware, software, a general purpose computer, a processor, or any combination thereof.
 10. A device manufacturing method, comprising: patterning a beam of radiation with a patterning device that is carried by a support; projecting the patterned beam of radiation onto a target portion of a substrate; determining data related to a height and a tilt profile of a surface of the patterning device with respect to the support; approximating the surface of the patterning device, the surface approximation defined by a non-linear function using the data and accounting for illumination effects due to curvature of an illumination slit, the non-linear function determined by: determining a first dataset corresponding to height and tilt data of the reticle on a first grid; determining a second dataset corresponding to a number of reticle stage set points on a second grid; and fitting the first dataset to the second dataset; and controlling a displacement of the support during exposure of the substrate in accordance with the non-linear function.
 11. A non-transient computer-readable medium having computer-executable instructions stored thereon that, when executed by a computer system, cause the computer system to facilitate manufacture of a device by the method as claimed in claim
 1. 12. A device manufacturing method comprising: exposing a substrate with a patterned beam of radiation formed by a reticle mounted on a displaceable reticle stage; determining a non-linear function for approximating a height and a tilt profile of a surface of the reticle with respect to the reticle stage by determining a first dataset corresponding to a height and a tilt data of the reticle on a first grid; determining a second dataset corresponding to a number of reticle stage set points on a second grid; and determining a fit of the first dataset to the second dataset, accounting for illumination effects due to curvature of an illumination slit; and controlling a displacement of the reticle stage during exposure of the substrate in accordance with the non-linear function.
 13. The method of claim 12, wherein the non-linear function is a quartic spline.
 14. A lithographic apparatus arranged to project a pattern from a reticle onto a substrate, the apparatus comprising: a displaceable reticle stage constructed and arranged to support the reticle, the reticle having a patterned side; a detector constructed and arranged to determine data related to a height and a tilt profile of a surface of the reticle with respect to the reticle stage; a computing device configured to approximate the height and the tilt profile by a non-linear function using the data, the non-linear function determined by: determining a first dataset corresponding to the data related to the height and the tilt profile of the surface of the reticle on a first grid; determining a second dataset corresponding to a number of reticle stage set points on a second grid; and determining a fit of the first dataset to the second dataset, accounting for illumination effects due to curvature of an illumination slit; and a controller constructed and arranged to control a displacement of the reticle stage during exposure of the substrate in accordance with the non-linear function.
 15. The apparatus of claim 14, wherein the non-linear function is a quartic spline.
 16. The method of claim 1, wherein the non-linear function is a quartic spline.
 17. The apparatus of claim 5, wherein the non-linear function is a quartic spline.
 18. The lithographic apparatus of claim 7, wherein the non-linear function is a quartic spline.
 19. The method of claim 10, wherein the non-linear function is a quartic spline. 